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Soutcome

Soutcome-fix

Fixing function for soutcome structures.

Signature
(soutcome-fix x) → new-x
Arguments: x — Guard (soutcomep x).
Returns: new-x — Type (soutcomep new-x).

Definitions and Theorems

Function: soutcome-fix$inline

(defun soutcome-fix$inline (x)
  (declare (xargs :guard (soutcomep x)))
  (let ((__function__ 'soutcome-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((cstate (cstate-fix (cdr (std::da-nth 0 (cdr x)))))
              (mode (mode-fix (cdr (std::da-nth 1 (cdr x))))))
           (cons :soutcome (list (cons 'cstate cstate)
                                 (cons 'mode mode))))
         :exec x)))

Theorem: soutcomep-of-soutcome-fix

(defthm soutcomep-of-soutcome-fix
  (b* ((new-x (soutcome-fix$inline x)))
    (soutcomep new-x))
  :rule-classes :rewrite)

Theorem: soutcome-fix-when-soutcomep

(defthm soutcome-fix-when-soutcomep
  (implies (soutcomep x)
           (equal (soutcome-fix x) x)))

Function: soutcome-equiv$inline

(defun soutcome-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (soutcomep acl2::x)
                              (soutcomep acl2::y))))
  (equal (soutcome-fix acl2::x)
         (soutcome-fix acl2::y)))

Theorem: soutcome-equiv-is-an-equivalence

(defthm soutcome-equiv-is-an-equivalence
  (and (booleanp (soutcome-equiv x y))
       (soutcome-equiv x x)
       (implies (soutcome-equiv x y)
                (soutcome-equiv y x))
       (implies (and (soutcome-equiv x y)
                     (soutcome-equiv y z))
                (soutcome-equiv x z)))
  :rule-classes (:equivalence))

Theorem: soutcome-equiv-implies-equal-soutcome-fix-1

(defthm soutcome-equiv-implies-equal-soutcome-fix-1
  (implies (soutcome-equiv acl2::x x-equiv)
           (equal (soutcome-fix acl2::x)
                  (soutcome-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: soutcome-fix-under-soutcome-equiv

(defthm soutcome-fix-under-soutcome-equiv
  (soutcome-equiv (soutcome-fix acl2::x)
                  acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-soutcome-fix-1-forward-to-soutcome-equiv

(defthm equal-of-soutcome-fix-1-forward-to-soutcome-equiv
  (implies (equal (soutcome-fix acl2::x) acl2::y)
           (soutcome-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-soutcome-fix-2-forward-to-soutcome-equiv

(defthm equal-of-soutcome-fix-2-forward-to-soutcome-equiv
  (implies (equal acl2::x (soutcome-fix acl2::y))
           (soutcome-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: soutcome-equiv-of-soutcome-fix-1-forward

(defthm soutcome-equiv-of-soutcome-fix-1-forward
  (implies (soutcome-equiv (soutcome-fix acl2::x)
                           acl2::y)
           (soutcome-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: soutcome-equiv-of-soutcome-fix-2-forward

(defthm soutcome-equiv-of-soutcome-fix-2-forward
  (implies (soutcome-equiv acl2::x (soutcome-fix acl2::y))
           (soutcome-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)